First of all thank you very much for your interest in OneNote Mobile for the iPhone, there has been a tremendous response thus far.
We have received reports from customers who are hitting an error on initial login, with the following message: "Login failed, error: 400".
The team has been investigating the issue and believe we have identified the cause. We are working on an update. However the underlying cause is an intermittent issue, due to overwhelming interest in the app. The workaround is to keep trying to sign in, once you get past this error then OneNote will sync without any problem.
Thank you for your patience and interest in OneNote, we all apologize for the inconvenience.